共查询到20条相似文献,搜索用时 312 毫秒
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A chord diagram is a set of chords of a circle such that no pair of chords has a common endvertex. A chord diagram is called nonintersecting if contains no crossing. For a chord diagram having a crossing , the expansion of with respect to is to replace with or . For a chord diagram , let be the chord expansion number of , which is defined as the cardinality of the multiset of all nonintersecting chord diagrams generated from with a finite sequence of expansions.In this paper, it is shown that the chord expansion number equals the value of the Tutte polynomial at the point for the interlace graph corresponding to . The chord expansion number of a complete multipartite chord diagram is also studied. An extended abstract of the paper was published (Nakamigawa and Sakuma, 2017) [13]. 相似文献
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Xiuyun Wang 《Discrete Mathematics》2017,340(12):3016-3019
The double generalized Petersen graph , and , , has vertex-set , edge-set . These graphs were first defined by Zhou and Feng as examples of vertex-transitive non-Cayley graphs. Then, Kutnar and Petecki considered the structural properties, Hamiltonicity properties, vertex-coloring and edge-coloring of , and conjectured that all are Hamiltonian. In this paper, we prove this conjecture. 相似文献
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Serhii Dyshko 《Discrete Mathematics》2018,341(11):2995-3002
For a finite vector space over , there are described all the pairs of multisets and of subspaces in such that for all the equality holds. 相似文献
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DP-coloring of a simple graph is a generalization of list coloring, and also a generalization of signed coloring of signed graphs. It is known that for each , every planar graph without is 4-choosable. Furthermore, Jin et al. (2016) showed that for each , every signed planar graph without is signed 4-choosable. In this paper, we show that for each , every planar graph without is 4-DP-colorable, which is an extension of the above results. 相似文献
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Elena Rubei 《Discrete Mathematics》2012,312(19):2872-2880
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Kiyoshi Ando 《Discrete Mathematics》2018,341(11):3003-3009
An edge of a -connected graph is said to be -contractible if the contraction of the edge results in a -connected graph. If every -connected graph with no -contractible edge has either or as a subgraph, then an unordered pair of graphs is said to be a forbidden pair for -contractible edges. We prove that is a forbidden pair for 6-contractible edges, which is an extension of a previous result due to Ando and Kawarabayashi. 相似文献
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The conservative number of a graph is the minimum positive integer , such that admits an orientation and a labeling of its edges by distinct integers in , such that at each vertex of degree at least three, the sum of the labels on the in-coming edges is equal to the sum of the labels on the out-going edges. A graph is conservative if . It is worth noting that determining whether certain biregular graphs are conservative is equivalent to find integer Heffter arrays.In this work we show that the conservative number of a galaxy (a disjoint union of stars) of size is for , , and otherwise. Consequently, given positive integers , , …, with for , we construct a cyclic -cycle system of infinitely many circulant graphs, generalizing a result of Bryant, Gavlas and Ling (2003). In particular, it allows us to construct a cyclic -cycle system of the complete graph , where . Also, we prove necessary and sufficient conditions for the existence of a cyclic -cycle system of , where is a 1-factor. Furthermore, we give a sufficient condition for a subset of to be sequenceable. 相似文献
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José E. Figueroa-López Yankeng Luo 《Stochastic Processes and their Applications》2018,128(12):4207-4245
In this article, we consider a Markov process , which solves a stochastic differential equation driven by a Brownian motion and an independent pure jump component exhibiting both state-dependent jump intensity and infinite jump activity. A second order expansion is derived for the tail probability in small time , where is the initial value of the process and . As an application of this expansion and a suitable change of the underlying probability measure, a second order expansion, near expiration, for out-of-the-money European call option prices is obtained when the underlying stock price is modeled as the exponential of the jump–diffusion process under the risk-neutral probability measure. 相似文献
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TextFor any given two positive integers and , and any set A of nonnegative integers, let denote the number of solutions of the equation with . In this paper, we determine all pairs of positive integers for which there exists a set such that for all . We also pose several problems for further research.VideoFor a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=EnezEsJl0OY. 相似文献
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Let be a prime power and be a positive integer. A subspace partition of , the vector space of dimension over , is a collection of subspaces of such that each nonzero vector of is contained in exactly one subspace in ; the multiset of dimensions of subspaces in is then called a Gaussian partition of . We say that contains a direct sum if there exist subspaces such that . In this paper, we study the problem of classifying the subspace partitions that contain a direct sum. In particular, given integers and with , our main theorem shows that if is a subspace partition of with subspaces of dimension for , then contains a direct sum when has a solution for some integers and belongs to the union of two natural intervals. The lower bound of captures all subspace partitions with dimensions in that are currently known to exist. Moreover, we show the existence of infinite classes of subspace partitions without a direct sum when or when the condition on the existence of a nonnegative integral solution is not satisfied. We further conjecture that this theorem can be extended to any number of distinct dimensions, where the number of subspaces in each dimension has appropriate bounds. These results offer further evidence of the natural combinatorial relationship between Gaussian and integer partitions (when ) as well as subspace and set partitions. 相似文献